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  <u1:Subject>How to use Qi - a complete guide</u1:Subject>
  <u1:Author>Dr M Tarver</u1:Author>
  <u1:Keywords>not freely available</u1:Keywords>
  <u1:Description>The definitive Qi exposition.</u1:Description>
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  <u1:Manager>Dr M Tarver</u1:Manager>
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</head>

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<div class=Section1>

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<table border=0 cellpadding=0 width="80%" bgcolor=white style='width:80.0%;
 mso-cellspacing:1.5pt;background:white;mso-padding-alt:0in 0in 0in 0in'>
 <tr>
  <td width="100%" style='width:100.0%;padding:0in 0in 0in 0in'>
  <p class=MsoTitle align=left style='margin-left:1.0in;text-align:left'><span
  style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  font-weight:normal;mso-bidi-font-weight:bold'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></p>
  <p class=MsoTitle align=left style='margin-left:1.0in;text-align:left'><span
  style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  font-weight:normal;mso-bidi-font-weight:bold'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></p>
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   border-collapse:collapse;border:none;mso-border-alt:solid windowtext .5pt;
   mso-padding-alt:0in 5.4pt 0in 5.4pt'>
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    padding:0in 5.4pt 0in 5.4pt'>
    <p class=MsoTitle align=left style='text-align:left'><span
    style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
    font-weight:normal;mso-bidi-font-weight:bold'><a href="QiPrograms.zip">Download
    Programs</a> <o:p></o:p></span></p>
    </td>
    <td width=492 valign=top style='width:368.75pt;border:solid windowtext .5pt;
    border-left:none;mso-border-left-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
    <p class=MsoTitle align=left style='text-align:left'><span
    style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
    font-weight:normal;mso-bidi-font-weight:bold'><a href="contents.htm">Go to
    Contents Page</a><o:p></o:p></span></p>
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  <p class=MsoTitle align=left style='margin-left:1.0in;text-align:left'><span
  style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  font-weight:normal;mso-bidi-font-weight:bold'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></p>
  <p class=MsoTitle align=left style='margin-left:1.0in;text-align:left'><span
  style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  font-weight:normal;mso-bidi-font-weight:bold'>Note that this HTML page was
  generated from Word 2000.<span style="mso-spacerun: yes">&nbsp; </span>Some
  of the code cannot be pasted into Qi. You are advised to download the program
  files through the above link.<o:p></o:p></span></p>
  <p class=MsoTitle align=left style='margin-left:1.0in;text-align:left'><span
  style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  font-weight:normal;mso-bidi-font-weight:bold'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></p>
  <p class=MsoTitle align=left style='margin-left:1.0in;text-align:left'><!--[if supportFields]><span
  style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  font-weight:normal;mso-bidi-font-weight:bold'><span style='mso-element:field-begin'></span></span><span
  style='font-family:"Microsoft Sans Serif";font-weight:normal;mso-bidi-font-weight:
  bold'><span style="mso-spacerun: yes">&nbsp;</span>XE &quot;Tarver&quot; </span><![endif]--><!--[if supportFields]><span
  style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  font-weight:normal;mso-bidi-font-weight:bold'><span style='mso-element:field-end'></span></span><![endif]--><span
  style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  font-weight:normal;mso-bidi-font-weight:bold'>Contents<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="reader.htm"><b>To the Reader</b></a><o:p></o:p></span></p>
  <u9:p></u9:p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="teacher.htm"><b>To the Teacher</b></a><u9:p></u9:p></span><b>
  </b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="acknowledgements.htm"><b>Acknowledgements</b></a><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span><span style="mso-spacerun:
  yes">&nbsp;</span><u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoHeading9 style='margin-left:1.0in'><span style='font-size:14.0pt;
  mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-ansi-language:EN-US'>Part I The Core Language<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt'><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'><a
  href="chap1.htm"><b>Chapter 1</b> <b>Beginnings<u9:p></u9:p></b></a></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt'><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span></span><o:p></o:p></p>
  <u9:p></u9:p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>1.1<b> </b>Declarative Programming<span style='mso-tab-count:
  1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span> </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>1.2 Mathematical Foundations<span style='mso-tab-count:
  1'>&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>1.3 The American Experience<span style='mso-tab-count:
  1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>1.4 The British Experience<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>1.5 SEQUEL &#8211; the predecessor of <span style='mso-bidi-font-style:
  italic'>Qi<u9:p></u9:p></span></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>1.6 The deficiencies of SEQUEL<span style='mso-tab-count:
  1'> </span><u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>1.7<span style="mso-spacerun: yes">&nbsp; </span>The
  Evolution of Qi in Britain<span style='mso-tab-count:1'> </span><u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.75in;margin-bottom:.0001pt;text-align:justify;text-indent:
  -.25in;mso-list:l0 level2 lfo2;tab-stops:list 1.75in'><![if !supportLists]>1.8<span
  style='font:7.0pt "Times New Roman"'> </span><![endif]><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'></span><span style='font-size:7.0pt'>&nbsp;
  </span><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>The Evolution of Qi in America<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="Chap2.htm"><b>Chapter 2</b> <b>The Qi<i> </i><span
  style='mso-bidi-font-style:italic'>Top Level</span><span style='mso-tab-count:
  1'> </span></b></a><u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>2.1 Starting Up<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>2.2 Applying Functions<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>2.3 Repeating Evaluations<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>2.4 Input/Output<span style='mso-tab-count:1'>&nbsp; </span><u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>2.5 Strict and Non-Strict Evaluation<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>2.6 Boolean Operations<span style='mso-tab-count:1'> </span><u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>2.7 Defining New Functions<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>2.8 Equations and Priority Rewrite Systems<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>2.9 A Fruit Machine Program<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap3.htm"><b>Chapter 3</b> <b>Recursion<span
  style='mso-tab-count:1'> </span></b></a></span><o:p></o:p></p>
  <u9:p></u9:p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span></span></b><span style='font-size:
  10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'>3.1
  Recursion and Infinity <span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>3.2 Tail and Linear Recursion<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>3.3 Tree Recursion<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>3.4 Guards<span style='mso-tab-count:
  4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>3.5 Mutual Recursion<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>3.6 Counting Change<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>3.7 Non-terminating Functions<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap4.htm"><b>Chapter 4 Lists</b></a></span><b><u9:p></u9:p>
  <o:p></o:p></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>4.1 Representing Lists in <span
  style='mso-bidi-font-style:italic'>Qi</span><span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>4.2 Building Lists with Cons<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>4.3 | is Shorthand for Cons<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>4.4 Head and Tail Access Parts of
  Lists<span style='mso-tab-count:1'>&nbsp; </span><span style='mso-tab-count:
  1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>4.5 Characters<span style='mso-tab-count:
  4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>4.6 Recursive List Processing<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>4.7 Local Assignments<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>4.8 Goldbach&#8217;s Conjecture Revisited<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap5.htm"><b>Chapter 5</b> <b>Higher Order
  Programming</b></a></span><b><u9:p></u9:p> </b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>5.1 Higher Order Functions<span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>5.2 Abstractions, Currying <span style='mso-tab-count:
  2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style="mso-spacerun:
  yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>and Partial Applications<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>5.3 Using Abstractions in <span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style="mso-spacerun:
  yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Higher Order Programs<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>5.4 Getting Rid of One-Off Functions<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>5.5 Taking Advantage of Similarities<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>5.6 Using Functions as Data<span style='mso-tab-count:
  3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap6.htm"><b>Chapter 6</b> <b>Assignments</b></a></span><o:p></o:p></p>
  <u9:p></u9:p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span></span></b><span style='font-size:
  10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'>6.1
  Simple Assignments<span style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>6.2 Arrays<span style='mso-tab-count:
  4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>6.3 Property Lists<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>6.4 Building Semantic Nets <span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap7.htm"><b>Chapter 7 Non-determinism</b></a></span><b><u9:p></u9:p>
  </b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span></span></b><span style='font-size:
  10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman";
  mso-bidi-font-weight:bold'>7.1 Non-deterministic Algorithms<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>7.2 Backward Chaining<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>7.3 Representing Proof Trees<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>7.4 Chronological Backtracking in <span
  style='mso-bidi-font-style:italic'>Qi<i><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></i></span></span><i>
  </i></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>7.5 Soundness and Completeness<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>7.6 Writing Refinement Rules: a
  Preview<span style='mso-tab-count:1'> </span><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>7.7 Selecting the Failure Object<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>7.8 The Static Elimination of
  Backtracking in <span style='mso-bidi-font-style:italic'>Qi</span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp; </span></span> </p>
  <span style='font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-family:
  "Times New Roman";color:black;mso-ansi-language:EN-US;mso-fareast-language:
  EN-US;mso-bidi-language:AR-SA'><br clear=all style='page-break-before:always'>
  </span>
  <p style='margin-left:1.0in'><a href="chap8.htm"><b><span style='font-size:
  10.0pt;mso-bidi-font-size:12.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>Chapter 8</span></b><span
  style='font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'> <b>Metaprograms</b></span></a><b><u9:p></u9:p>
  </b><span style='font-size:11.0pt;mso-bidi-font-size:10.0pt'><o:p></o:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>8.1 Building a Parser in <span
  style='mso-bidi-font-style:italic'>Qi</span><span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>8.2 Recursive Descent Parsing in <span
  style='mso-bidi-font-style:italic'>Qi</span><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>8.3 The <b>eval</b> Function<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap9.htm"><b>Chapter 9 Writing Good Programs</b></a></span><b><u9:p></u9:p>
  </b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoHeading9 style='margin-left:1.0in'><span style='font-size:14.0pt;
  mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-ansi-language:EN-US'>Part II Working with Types<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap10.htm"><b>Chapter 10</b> <b>Types</b></a></span><b><u9:p></u9:p>
  </b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span></span></b><span style='font-size:
  10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'>10.1
  Types and Type Security<span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>10.2 Modifying the Read-Evaluate-Print
  Loop<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>10.3 Base Types and Operators<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>10.4 The list Type Operator<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>10.5 The Function Space Operator </span><span
  lang=EN-GB style='font-size:10.0pt;font-family:Symbol;mso-ansi-language:EN-GB;
  mso-bidi-font-weight:bold'>�<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  lang=EN-GB style='mso-ansi-language:EN-GB'> </span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>10.6 The Product Type Operator *<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>10.7 Polytypes<span style='mso-tab-count:
  4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>10.8 Using Type Checking<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>10.9 Loading Files<span
  style='mso-tab-count:4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap11.htm"><b>Chapter 11 Defining Types</b></a></span><b><u9:p></u9:p>
  </b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span></span></b><span style='font-size:
  10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman";
  mso-bidi-font-weight:bold'>11.1 Enumeration Types<span style='mso-tab-count:
  2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>11.2 Side Conditions<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>11.3 Synonyms<span style='mso-tab-count:
  4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>11.4 Left and Right Rules<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>11.5 Defining Recursive Types<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>11.6 Simulating a Calculator<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>11.7 Verified Objects<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>11.8 Defining Type Operators<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>11.9 Working with Functions Other than
  Cons<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>11.10 Subtypes<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>11.11 Type Checking Assignments<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>11.12 Structures<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman";mso-bidi-font-weight:bold'>11.13
  Abstract Datatypes<u9:p></u9:p><o:p></o:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:.5in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span><br clear=all style='page-break-before:
  always'>
  </span></b><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'><a href="chap12.htm"><b>Chapter 12
  Compiling Qi</b></a></span><b><u9:p></u9:p> </b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>12.1 The Lambda Calculus<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>12.2 Reasoning with the Lambda Calculus<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>12.3 The Church-Rosser Theorems<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>12.4 Representing Things in Lambda
  Calculus<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>12.5 Recursion and the Y-combinator<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>12.6 From Lambda Calculus to
  Functional Programming<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>12.7 The Compilation of <span
  style='mso-bidi-font-style:italic'>Qi</span> to </span><span
  style='font-family:BrushScrD'>L</span><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'><span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>12.8 The Compilation of </span><span
  style='font-family:BrushScrD'>L</span><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'>
  to Lambda Calculus<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:8.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap13.htm"><b>Chapter 13 Type Checking as Proof</b></a></span><o:p></o:p></p>
  <u9:p></u9:p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>13.1 The <span style='mso-bidi-font-style:
  italic'>Qi</span> Type System<span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>13.2 Type Checking Applications<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>13.3 Choosing Values by Unification<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>13.4 Type Checking Abstractions<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>13.5 Polymorphic Functions<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>13.6 Typing Special Forms<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>13.7 Internal Forms<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>13.8 Mutual Recursion<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>13.9 Global Variables<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>13.10 Procedure </span><span
  style='font-family:BrushScrD'>T</span><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'>*<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>13.11 From Type Checking to Automated
  Deduction<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:8.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoHeading9 style='margin-left:1.0in'><span style='font-size:14.0pt;
  mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-ansi-language:EN-US'>Part III Automated Reasoning,
  Expert Systems and Intelligent Agents<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:8.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap14.htm"><b>Chapter 14 Proof Systems</b></a></span><b><u9:p></u9:p>
  </b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>14.1 Building Automated Theorem
  Provers<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>14.2 Proof Systems<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>14.3 Propositional Calculus<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>14.4 Propositional Calculus in <span
  style='mso-bidi-font-style:italic'>Qi</span><span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>14.5 The Proof Tool<span style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>14.6 Solving Goals in <span style='mso-bidi-font-style:
  italic'>Qi</span><span style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>14.7 A Decision Procedure for PC<span style='mso-tab-count:
  1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>14.8 Expressing our Heuristics for PC in <span
  style='mso-bidi-font-style:italic'>Qi</span><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>14.9 Special Variables<span style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>14.10 Modal Logic and Non-Monotonic Logic<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></p>
  <span style='font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-family:
  "Times New Roman";color:black;mso-ansi-language:EN-US;mso-fareast-language:
  EN-US;mso-bidi-language:AR-SA'><br clear=all style='page-break-before:always'>
  </span>
  <p style='margin-left:1.0in'><a href="chap15.htm"><b><span style='font-size:
  10.0pt;mso-bidi-font-size:12.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>Chapter 15 First Order Logic</span></b></a><u9:p></u9:p>
  <span style='font-size:11.0pt;mso-bidi-font-size:10.0pt'><o:p></o:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>15.1 The Syntax and Proof Theory of
  FOL<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>15.2 Expressing FOL in <span
  style='mso-bidi-font-style:italic'>Qi</span><span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>15.3 Coding Quantifier Refinement
  Rules<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>15.4 A Simple Proof in First-Order
  Logic<span style='mso-tab-count:1'>&nbsp; </span><span style='mso-tab-count:
  1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>15.5 Automating Proof in FOL<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>15.6 Skolemisation<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>15.7 Prenex Form<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>15.8 Rectification<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>15.9 Universal Quantifiers and
  Unification<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>15.10 Skolemisation in Sequent Systems<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>15.11 Clause Form<span
  style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>15.12 The Refinement Rules for
  AUTOFOL<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>15.13 Representing Bindings with the
  Notepad<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>15.14 Some AUTOFOL Proofs<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>15.15 The Incompleteness of AUTOFOL<span
  style='mso-tab-count:1'> </span><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>15.16 A Complete AUTOFOL<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>15.17 Optimising AUTOFOLC<span
  style='mso-tab-count:6'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap16.htm"><b>Chapter 16 Expert Systems</b></a></span><b><u9:p></u9:p>
  </b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style="mso-spacerun:
  yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
  </span>16.1 Diagnosis as Explanation<span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>16.2 Explanations and Proof Trees<span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>16.3 Coding BEP in <span
  style='mso-bidi-font-style:italic'>Qi</span><span style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-weight:bold'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>16.4 micro-MYCIN in <span
  style='mso-bidi-font-style:italic'>Qi</span><span style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><a href="chap17.htm"><b>Chapter 17 Intelligent Agents</b></a></span><b><u9:p></u9:p>
  </b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>17.1 Modeling Commuters With
  Intelligent Agents<u9:p></u9:p></span></p>
  <p class=MsoHeading9 style='margin-left:1.0in;text-align:justify;text-indent:
  .5in'><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman";mso-ansi-language:EN-US;font-weight:
  normal;mso-bidi-font-weight:bold'>17.2 The Story of Agent 95<span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-left:1.0in'><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span>17.3 Mathematical Modeling vs.
  Intelligent Agents<span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span>
  </p>
  <span lang=EN-GB style='font-size:12.0pt;font-family:"Times New Roman";
  mso-fareast-font-family:"Times New Roman";color:black;mso-ansi-language:EN-GB;
  mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><br clear=all
  style='mso-special-character:line-break;page-break-before:always'>
  </span>
  <p><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></p>
  <p class=MsoHeading9 style='margin-left:1.0in'><span style='font-size:14.0pt;
  mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-ansi-language:EN-US'>Appendices<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>Appendix A</span></b><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'> <span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span><a href="appendixA.htm">System
  Functions and their Types in Qi<span style='mso-tab-count:1'>&nbsp; </span></a><u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>Appendix B<span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>
  </span></b><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'><a href="appendixB.htm">Installing
  and Using Qi under Lisp<!--[if supportFields]><span style='mso-element:field-begin'></span>
  XE &quot;Lisp&quot; <![endif]--><!--[if supportFields]><span
  style='font-size:11.0pt;mso-bidi-font-size:10.0pt;font-family:"Times New Roman"'><span
  style='mso-element:field-end'></span></span><![endif]--></a><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></b></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>Appendix C <span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span></span></b><span style='font-size:
  10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'><a
  href="appendixC.htm">The Syntax of Qi<i> </i>and the Qi Printer and Reader</a><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>Appendix D</span></b><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'> <span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span><a href="appendixD.htm">The Semantics
  of<span style="mso-spacerun: yes">&nbsp; </span><span style='font-size:11.0pt;
  mso-bidi-font-size:10.0pt;font-family:BrushScrD;mso-bidi-font-style:italic'>L<u9:p></u9:p></span></a></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>Appendix E</span></b><span style='font-size:18.0pt;
  mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'> <span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style="mso-spacerun: yes">&nbsp;</span><a
  href="appendixE.htm">The Type Security of the<span style='font-size:18.0pt;
  mso-bidi-font-size:10.0pt'> </span><span style='font-size:11.0pt;mso-bidi-font-size:
  10.0pt;font-family:BrushScrD;mso-bidi-font-style:italic'>L </span>Type System</a>
  <span style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>Appendix F</span></b><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'><span
  style="mso-spacerun: yes">&nbsp; </span><span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span
  style='font-family:BrushScrD;mso-bidi-font-style:italic'><span
  style="mso-spacerun: yes">&nbsp;</span><a href="appendixF.htm">T<span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-style:normal'> and the</span><span
  style='font-size:18.0pt;mso-bidi-font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman";mso-bidi-font-style:normal'> </span>L <span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman";mso-bidi-font-style:normal'>Type System<u9:p></u9:p></span></a></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>Appendix G</span></b><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'><span
  style="mso-spacerun: yes">&nbsp; </span><span style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span><a href="appendixG.htm">A Case Study:
  an<span style='font-size:18.0pt;mso-bidi-font-size:10.0pt'> </span><span
  style='font-size:11.0pt;mso-bidi-font-size:10.0pt;font-family:BrushScrD;
  mso-bidi-font-style:italic'>L </span>Interpreter in Qi</a><u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>Appendix H</span></b><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'> <span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span><a href="appendixH.htm">The Qi
  Debugging Environment<span style='mso-tab-count:1'> </span></a><u9:p></u9:p></span>
  </p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.5in;margin-bottom:.0001pt;text-align:justify;text-indent:
  -.5in'><b><span style='font-size:10.0pt;font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>Appendix I</span></b><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style="mso-spacerun: yes">&nbsp; </span><span
  style='mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style="mso-spacerun: yes">&nbsp;</span><a href="appendixI.htm">Qi/Tk and the
  IFPE Project</a></span><!--[if supportFields]><span style='font-size:10.0pt;
  font-family:"Microsoft Sans Serif";mso-bidi-font-family:"Times New Roman"'><span
  style='mso-element:field-begin'></span></span><span style='font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'> XE &quot;</span><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>Free University</span><span style='font-family:"Microsoft Sans Serif";
  mso-bidi-font-family:"Times New Roman"'>&quot; </span><![endif]--><!--[if supportFields]><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-element:field-end'></span></span><![endif]--><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'><span style='mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
  style='mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><u9:p></u9:p></span><span
  style="mso-spacerun: yes">&nbsp;</span></p>
  <p class=MsoNormal style='margin-top:0in;margin-right:-.35pt;margin-bottom:
  0in;margin-left:1.0in;margin-bottom:.0001pt;text-align:justify'><span
  style='font-size:10.0pt;font-family:"Microsoft Sans Serif";mso-bidi-font-family:
  "Times New Roman"'>&nbsp;<u9:p></u9:p></span></p>
  </td>
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